Taiwanese Journal of Mathematics
- Taiwanese J. Math.
- Volume 9, Number 2 (2005), 187-200.
GLOBAL AND NON-GLOBAL SOLUTIONS OF A NONLINEAR PARABOLIC EQUATION
We study the global and non-global existence of positive solutions of a nonlinear parabolic equation. For this, we consider the forward and backward self-similar solutions of this equation. We obtain a family of radial symmetric global solutions which tend to zero as the time tends infinity. Next, we show that there are initial data for which the corresponding solutions blow up in finite time. Finally, we also construct some self-similar single-point blow-up patterns with different oscillations.
Taiwanese J. Math., Volume 9, Number 2 (2005), 187-200.
First available in Project Euclid: 18 July 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions 35B40: Asymptotic behavior of solutions 35K55: Nonlinear parabolic equations
Guo, Jong-Shenq; Lin Guo, Yung-Jen; Wang, Chi-Jen. GLOBAL AND NON-GLOBAL SOLUTIONS OF A NONLINEAR PARABOLIC EQUATION. Taiwanese J. Math. 9 (2005), no. 2, 187--200. doi:10.11650/twjm/1500407795. https://projecteuclid.org/euclid.twjm/1500407795